The plunge in the Turkish lira hasn’t just rippled into other emerging markets: It is also putting an unwelcome spotlight back on the euro.

The European currency has been trapped for nearly three months in a relatively narrow range between $1.15 and $1.18. But it has now broken downward to $1.138, its lowest level for more than a year, as the collapse in the lira—now down 45% this year against the U.S. dollar—has accelerated. The Turkish central bank has taken measures to provide liquidity but hasn’t delivered the big interest-rate...